**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Publication# Stochastic approximation methods for PDE constrained optimal control problems with uncertain parameters

Abstract

This thesis work focuses on optimal control of partial differential equations (PDEs) with uncertain parameters, treated as a random variables. In particular, we assume that the random parameters are not observable and look for a deterministic control which is robust with respect to the randomness. The theoretical framework is based on adjoint calculus to compute the gradient of the objective functional. Unlike the deterministic case, we have a set of PDEs indexed by some uncertain parameters and the objective functional we consider includes some risk measure (e.g. expectation, variance, quantile (Value at Risk), ...) to take care of all realizations of our uncertain parameters. Introducing the regular class of coherent risk measure, results of convergence and regularity of the optimal control have been derived.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related concepts (3)

Optimal control

Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the moon with minimum fuel expenditure.

Partial differential equation

In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similar to how x is thought of as an unknown number to be solved for in an algebraic equation like x2 − 3x + 2 = 0. However, it is usually impossible to write down explicit formulas for solutions of partial differential equations.

Parameter

A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc. Parameter has more specific meanings within various disciplines, including mathematics, computer programming, engineering, statistics, logic, linguistics, and electronic musical composition.